Question: A group of adults and kids went to see a movie. Tickets cost $$5.50$ each for adults and $$3.50$ each for kids, and the group paid $$53.50$ in total. There were $5$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Answer: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${5.5x+3.5y = 53.5}$ ${x = y-5}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-5}$ for $x$ in the first equation. ${5.5}{(y-5)}{+ 3.5y = 53.5}$ Simplify and solve for $y$ $ 5.5y-27.5 + 3.5y = 53.5 $ $ 9y-27.5 = 53.5 $ $ 9y = 81 $ $ y = \dfrac{81}{9} $ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into ${x = y-5}$ to find $x$ ${x = }{(9)}{ - 5}$ ${x = 4}$ You can also plug ${y = 9}$ into ${5.5x+3.5y = 53.5}$ and get the same answer for $x$ ${5.5x + 3.5}{(9)}{= 53.5}$ ${x = 4}$ There were $4$ adults and $9$ kids.